I had an email exchange with Rob regarding n-gonal pyramids, an edited version of which is repeated below for the benefit of Forum members.

On 5/07/2015, I wrote:

"I've been attempting to produce various pyramids in Great Stella with different bases - up to a 20-gon. Unfortunately I get the error message "Illegal pyramid base" whenever I use the N-gonal Pyramid dialog. Similarly with cupolae."

Rob's reply a few hours later the same day

"It's trying to make a pyramid or cupola with regular faces, which isn't possible with a 20-gon base, for example.

Another way to do it is to start with a 20-gon prism, then augment one side with a pyramid "Poly->Augment Polyhedron". Then you can adjust the size as you wish during the augmentation preview, hit Enter to finalise it, then extract the pyramid from the base to leave just the pyramid."

Rob also pointed out the benefits of posting questions like this to the Forum, hence this posting!

Of course, a 20-sided pyramid with something like a {20/9} star icosagon base can have equilateral sides.

In general, for an {n/m}star base, n/m < 6 will allow a uniform star pyramid.
Also, n and m must be co-prime (no common factor) or you get a compound, and m < n/2 or you get a backward duplicate of one with smaller n.

So for the icosagon the solutions are {20/7} and {20/9}.

Note also that for n < 6 we get valid solutions for m = 1 (i.e. convex uniform pyramids).